Abstract
In this paper we generalise the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems to the additive Schwarz waveform relaxation (ASWR) for parabolic problems. The domain decomposition is in space and time. We show that our technique: 1) is a direct solver that requires at most four solves per subdomain in the case of a one space dimension linear parabolic problem with time independent coefficients; 2) can be applied easily to multidimensional problems, provided that the operator is separable in space; 3) is an efficient iterative procedure for parabolic problems that are weak non-linear perturbations of linear operators with time independent coefficients; 4) provides a rigorous framework to optimise the parallel implementation on a slow network of computers.
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